Answer:
The answer is -1 or 9
The quadratic equation is ax² + bx + c = 0. But, by completing the square we turn it into: a(x + d)² + e = 0, where:
d = b/2a
e = c - b²/4a
Our quadratic equation is x² - 8x = 9, which is after rearrangement:
x² - 8x - 9 = 0
So, a = 1, b = -8, c = -9
Let's first calculate d and e:
d = b/2a = -8/(2 * 1) = -8/2 = -4
e = c - b²/4a = -9 - (-8)²/(4 * 1) = -9 - 64/4 = -9 - 16 = -25
By completing the square we have:
a(x + d)² + e = 0
1(x + (-4))² + (-25) = 0
(x - 4)² - 25 = 0
(x - 4)² = 25
⇒ x - 4 = √25
Since √25 can be either -5 or +5 , then:
x - 4 = -5 or x - 4 = 5
x = -5 + 4 or x = 5 + 4
x = -1 or x = 9
Step-by-step explanation:
Large Rectangles: 2 x 3 x 6
Medium Rectangles: 2 x 2 x 6
Small Rectangles: 2 x 2 x 3
Surface Area: 72 cm^2
The number of remaining problems is:
30-20 = 10 problems.
The amount of time remaining is:
40-25 = 15minutes
For the first 20 problems the time per problem is:
t1 = 25/20 = 5/4 minutes
For the remaining problems the time per problem is:
t2 = 15/10 = 3/2 minutes
Answer:
you will be able to spend about 3/2 minutes on each remaining problem
Answer:
Let the width of the poster = X inches
SO, the length of the poster = X+6 inches
Let the perimeter of the rectangular poster = 188 inches
Step-by-step explanation:
x+X+6 = 188
2x+6 = 188
transfer + 6 to right side
2x = 188-6
2x = 182
X = 182/2
X = 91
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